Autonomous individuals establish a structural complex system through pairwise connections and interactions. Notably, the evolution reflects the dynamic nature of each complex system since it recodes a series of temporal changes from the past, the present into the future. Different systems follow distinct evolutionary trajectories, which can serve as distinguishing traits for system classification. However, modeling a complex system's evolution is challenging for the graph model because the graph is typically a snapshot of the static status of a system, and thereby hard to manifest the long-term evolutionary traits of a system entirely. To address this challenge, we suggest utilizing a heat-driven method to generate temporal graph augmentation. This approach incorporates the physics-based heat kernel and DropNode technique to transform each static graph into a sequence of temporal ones. This approach effectively describes the evolutional behaviours of the system, including the retention or disappearance of elements at each time point based on the distributed heat on each node. Additionally, we propose a dynamic time-wrapping distance GDTW to quantitatively measure the distance between pairwise evolutionary systems through optimal matching. The resulting approach, called the Evolution Kernel method, has been successfully applied to classification problems in real-world structural graph datasets. The results yield significant improvements in supervised classification accuracy over a series of baseline methods.

翻译：自主个体通过成对连接与交互构建结构化复杂系统。值得注意的是，演化通过编码从过去、现在到未来的系列时序变化，反映了每个复杂系统的动态本质。不同系统遵循各异的演化轨迹，这些轨迹可作为区分系统类型的特征。然而，用图模型对复杂系统的演化进行建模极具挑战性，因为图通常仅表征系统静态状态的快照，难以完整呈现系统的长期演化特征。针对这一难题，我们提出利用热驱动方法生成时序图增强。该方法融合基于物理学的热核与DropNode技术，将每个静态图转化为时序图序列。基于各节点分布的热量，该方案可有效描述元素在每个时间点的存续或消失等系统演化行为。此外，我们提出动态时间弯曲距离GDTW，通过最优匹配量化成对演化系统间的距离。由此构建的"演化核"方法已成功应用于真实结构图数据集的分类问题。实验结果表明，相较于一系列基线方法，本方法在监督分类准确率上取得了显著提升。